2024/08/03 by Xingjian Li, Li, Xingjian, Ting-Chun Lin +3 · 3 citations
Computer Science · Engineering · #Advanced Wireless Communication Techniques #Error Correcting Code Techniques #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.2408.01769
openalex publication_date 2024/08/03 · openalex created_date 2024/10/14 · openalex updated_date 2026/07/28
Geometrically local quantum codes, comprised of qubits and checks embedded in ℝD with local check operators, have been a subject of significant interest. A key challenge is identifying the optimal code construction that maximizes both dimension and distance. Recent advancements have produced several constructions, but these either depend on specific good quantum low-density parity-check (qLDPC) codes or are limited to three dimensions. In this work, we introduce a construction that can transform any good qLDPC code into an optimal geometrically local quantum code. Our approach hinges on a novel procedure that extracts a two-dimensional structure from an arbitrary three-term chain complex. We expect that this procedure will find broader applications in areas such as weight reduction and the geometric realization of chain complexes.